Question

"True or False: If a derivative function is not constant, then the derivative must take on some irrational values."

Answer 1

@Ultrilliam o:

Answer 2

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Answer 3

Answer is no.
Suppose it's true,
then the derivative function must be continuous
(since differentiable functions are continuous)
but continuous functions require no "gaps" so it must include both rational and irrational numbers

Answer 4

ok

Answer 5

OOPS, I meant to say the original function must be continuous, but yeah same thing.

Gotta be politically correct especially in math analysis.

Answer 6

and Darboux theorem

Answer 7

Be owner, chico *-*